A fair coin is tossed 6 times. For what value of k is the conditional probability that Pr(x<=k I x<=K+1) is a max? Assuming k = 1, 2, 3, 4, 5; x = number of heads tossed

X ~ Binomial(n = 6, p = 1/2).

The conditional probability is equal to $\displaystyle \frac{\Pr(X \leq k)}{\Pr(X \leq k + 1)}$ (why?). Now check each value of k to find the one that gives the maximum value. If you need more help, please post your work and say where you get stuck.